Posted on: 20th Mar 2025

CVE1222 Structural Analysis 1: Stress, Strain, Stability, and Truss Evaluation Coursework (AY24/25)

PART 1: STRESS TRANSFORMATION

A wooden beam is loaded with several point forces, as depicted in Fig.1. It is supported by a pin at B and a smooth support (roller) at A. Grains of wood in the beam make an angle of 60ยฐ with the horizontal direction. Determine the normal and shear stresses that act perpendicular and parallel to the grains, respectively, at points C and D.

CVE1222 Structural Analysis 1

PART 2: STRAIN TRANSFORMATION

A 60ยฐ strain rosette is mounted on the surface of a steel bracket to measure the strain state, as shown in Fig. 2. The following readings are obtained for each strain gauge: ๐œ€๐œ€๐‘Ž๐‘Ž = โˆ’440 ร— 10โˆ’6, ๐œ€๐œ€๐‘๐‘ = 1120 ร— 10โˆ’6 and ๐œ€๐œ€๐‘๐‘ = 175 ร— 10โˆ’6. The material properties of the steel bracket are: Youngโ€™s modulus E = 200GPa, and Poissonโ€™s ratio ฮฝ = 0.3.

(1) Determine the principal strains and the associated orientations.

(2) Determine the maximum in-plane shear strain and the associated normal strain.

(3) Determine the principal stresses and the associated orientations.

CVE1222 Structural Analysis 1

PART 3: STATIC DETERMINACY

Classify each of the structures in Fig. 3 as statically determinate, statically indeterminate or unstable. If statically indeterminate, specify the degree of indeterminacy.

CVE1222 Structural Analysis 1

PART 4: PLANAR TRUSS ANALYSIS

A truss is loaded with two point forces at its joints, as shown in Fig. 4. Use Method of Joints and/or Method of Sections to obtain the member force for all truss members. State if the members are in tension or compression.

CVE1222 Structural Analysis 1

[Hints: You may firstly identify all zero-force members to simplify the truss. Then, use Method
of Joints if at a joint there are only 1 or 2 unknowns. When using Method of Section, choose
the section path so that there are at most 3 unknowns.]

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